61A Lecture 5 Optional discussion to promote mastery of core - - PDF document

61A Lecture 5

Friday, January 30

Announcements

• Quiz 1 scores will be posted eventually, but you already know what you'll get

• Guerrilla Section 1 on higher-order functions is on Saturday 1/31 in 271 Soda

• Small-group tutoring begins next week! Apply online by Sunday if you want a (free) tutor
• Homework 2 (which is small) is due Monday 2/2 at 11:59pm
• Project 1 (which is BIG) us due Thursday 2/5 at 11:59pm
• Midterm 1 on Monday 2/9 7pm-9pm

Environments for Higher-Order Functions

Environments Enable Higher-Order Functions

(Demo)

Environment diagrams describe how higher-order functions work! Functions are first-class: Functions are values in our programming language Higher-order function: A function that takes a function as an argument value or
 A function that returns a function as a return value

Names can be Bound to Functional Arguments

• Create a new frame
• Bind formal parameters


(f & x) to arguments

• Execute the body:


return f(f(x)) Interactive Diagram

Environments for Nested Definitions

(Demo)

Environment Diagrams for Nested Def Statements

• Every user-defined function has

a parent frame (often global)

• The parent of a function is the

frame in which it was defined

• Every local frame has a parent

frame (often global)

• The parent of a frame is the

parent of the function called Nested def

Interactive Diagram

How to Draw an Environment Diagram

When a function is defined: Create a function value: func <name>(<formal parameters>) [parent=<label>] Its parent is the current frame.
 
 
 Bind <name> to the function value in the current frame When a function is called:

• 1. Add a local frame, titled with the <name> of the function being called.
• 2. Copy the parent of the function to the local frame: [parent=<label>]
• 3. Bind the <formal parameters> to the arguments in the local frame.
• 4. Execute the body of the function in the environment that starts with the local frame.

Local Names

(Demo)

Local Names are not Visible to Other (Non-Nested) Functions

“y” is not found “y” is not found, again Error

• An environment is a sequence of frames.
• The environment created by calling a top-level function (no def within def)

consists of one local frame, followed by the global frame.

Interactive Diagram

Function Composition

(Demo)

The Environment Diagram for Function Composition

Return value of make_adder is an argument to compose1

Interactive Diagram

Lambda Expressions

(Demo)

Lambda Expressions

>>> x = 10 >>> square = x * x >>> square = lambda x: x * x >>> square(4) 16 An expression: this one evaluates to a number Also an expression: evaluates to a function that returns the value of "x * x" with formal parameter x A function Lambda expressions are not common in Python, but important in general Important: No "return" keyword! Must be a single expression

Lambda expressions in Python cannot contain statements at all!

Lambda Expressions Versus Def Statements

square = lambda x: x * x def square(x): return x * x

VS

• Both create a function with the same domain, range, and behavior.
• Both functions have as their parent the frame in which they were defined.
• Both bind that function to the name square.
• Only the def statement gives the function an intrinsic name.

The Greek letter lambda

Currying

Function Currying

def make_adder(n): return lambda k: n + k >>> make_adder(2)(3) 5 >>> add(2, 3) 5 There's a general relationship between these functions Curry: Transform a multi-argument function into a single-argument, higher-order function

(Demo)